I imagine the upgrades are because of the small potency of the lower level spells.
They can't give the lower level spells too high of a potency that would make them work well at higher levels. But if you tried to level with just, say, Aero and Stone 1, it would take you ages to kill anything. It was a pretty noticeable jump when I got Stone 3 in the speed of me killing things - I just got to 60 about a week ago, so it's all fresh for me still. Spamming Holy is pretty MP inefficient since it will chew through your entire bar in a few casts and not really do that much for you.
Is it possible that they want healers to DPS a bit? Sure. Assize doing damage was probably added for that purpose, but it's also not only for damage. But first and foremost, healers are given damaging spells to progress through solo content.
I think it is a good thing to weave in some DPS when you're healing, but I don't think a healer is bad for not DPSing. And I think it's really pitiful when a party really -needs- a healer's DPS in order to kill things.